The glass-half-full type’s answer would be that the Beijing student population studies slightly different material (for instance, some will also be preparing for US college applications), hence a different test.
My (more cynical) guess is that Beijing has a different, easier test because the people who make Chinese education policy live in Beijing, as do many Communist Party higher-ups, large numbers of government functionaries who are also reliable supporters of the Party, and the military top brass whose loyalty matters to Party leadership.